What is (\partial)/(\partial x)(6e^ysin(4x)+3y-2xy) ?

The answer to (\partial)/(\partial x)(6e^ysin(4x)+3y-2xy) is 24e^ycos(4x)-2y

Popular >

(\partial)/(\partial x)(6e^ysin(4x)+3y-2xy)

\frac{\partial}{\partial x} (6 e^{y} sin (4 x) + 3 y - 2 x y)

24 e^{y} cos (4 x) - 2 y

Solution steps

\frac{\partial}{\partial x} (6 e^{y} sin (4 x) + 3 y - 2 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (6 e^{y} sin (4 x)) + \frac{\partial}{\partial x} (3 y) - \frac{\partial}{\partial x} (2 x y)

\frac{\partial}{\partial x} (6 e^{y} sin (4 x)) = 24 e^{y} cos (4 x)

\frac{\partial}{\partial x} (3 y) = 0

\frac{\partial}{\partial x} (2 x y) = 2 y

= 24 e^{y} cos (4 x) + 0 - 2 y

Simplify

= 24 e^{y} cos (4 x) - 2 y

\int 2 - x^{2} - x d x

\int \frac{10000 - 5000 x}{( x ^{2} - 4 x + 5 ) ^{2}} d x

n = 0 \sum \infty \frac{n !}{10 4 ^{n}}

f (x) = \frac{( 1 )}{( 1 + x ^{2} )}

\int \frac{e ^{t} cos ( e ^{t} )}{3 + 3 sin ( e ^{t} )} d t

What is (\partial)/(\partial x)(6e^ysin(4x)+3y-2xy) ?
The answer to (\partial)/(\partial x)(6e^ysin(4x)+3y-2xy) is 24e^ycos(4x)-2y